The Unmixing Problem

High-gain adaptive stabilization of minimum-phase linear systemsraises the so-called unmixing problem: finding a finite setA of matrices, with the property that for any M GL(n), (AM)C₊ for at least one A . First, some preliminary results will be given, leading up to a non-constructive proofof the existence of such finiteA's. For the cases n = 2 and3, a fairly satisfying solution is presented. In higher dimensions,the situation is more complicated, and negative results aregiven. Based on the Euler angles for O(n), an explicit solutionis given for arbitrary n.